################################################################################
# CAS Data Engineering Modul 2 - "Crypto Gruppe" #
# Time Series Analysis of Bitcoin Prices with R #
# -> Statistical Tests and ARIMA Experiment <- #
# #
# 09 July 2021 #
# #
################################################################################
# References:
#
# SUMNER, T. 14/11/2019. Forecasting Bitcoin in R.
# Available from: https://rstudio-pubs-static.s3.amazonaws.com/549884_39fa223876e448608b7a7fa79337feba.html
#
# JAQUART, P. DANN, D. WEINHARDT, Ch. Short-term bitcoin market prediction via machine learning
# Available online at www.sciencedirect.com
#
# URAS, N. MARCHESI, L. MARCHESI, M. TONELLI, R. Forecasting Bitcoin closing price series using linear regression and neural networks models
# Uras et al. (2020), PeerJ Comput. Sci., DOI 10.7717/peerj-cs.279
#
#
################################################################################
# Remove Data & Libraries
rm(list=ls())
# Load Libraries
library(foreign)
library(psych)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.2 v stringr 1.4.0
## v tidyr 1.1.3 v forcats 0.5.1
## v readr 1.4.0
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x ggplot2::%+%() masks psych::%+%()
## x ggplot2::alpha() masks psych::alpha()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
library(zoo)
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(lubridate)
##
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union
library(fpp2)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## -- Attaching packages ---------------------------------------------- fpp2 2.4 --
## v forecast 8.15 v expsmooth 2.3
## v fma 2.4
## -- Conflicts ------------------------------------------------- fpp2_conflicts --
## x ggplot2::%+%() masks psych::%+%()
## x ggplot2::alpha() masks psych::alpha()
library(astsa)
##
## Attaching package: 'astsa'
## The following objects are masked from 'package:fma':
##
## chicken, sales
## The following object is masked from 'package:forecast':
##
## gas
## The following object is masked from 'package:fpp2':
##
## oil
## The following object is masked from 'package:psych':
##
## scatter.hist
library(plotly)
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
library(tseries)
# Initial configurations
# Set default font
windowsFonts(Georgia = windowsFont("Georgia"))
## Set Original plot theme
my_theme = theme(panel.grid = element_line(color = '#e6e6e6'),
panel.background = element_rect(fill = 'white'),
plot.title = element_text(hjust = .5, size = 28,
colour = '#ffa500'),
text = element_text(family = 'Georgia'),
axis.text = element_text(size = 10),
axis.title = element_text(size = 18, family = 'Georgia',
face = 'bold'),
axis.line = element_line(colour = '#737373', size = 1),
strip.background = element_rect(colour = "black",
fill = "white"),
strip.text = element_text(face = 'bold'))
# Read Data
# Read Original Bitcoin Dataset
bitcoin <- read_csv('bitcoin_full_daily_prices.csv')
##
## -- Column specification --------------------------------------------------------
## cols(
## .default = col_double(),
## Date = col_date(format = ""),
## sentiment_elon = col_character(),
## sentiment_bitcoin = col_character()
## )
## i Use `spec()` for the full column specifications.
names(bitcoin)
## [1] "Date" "Open" "High"
## [4] "Low" "Close" "WeightedPrice"
## [7] "Volume" "SMA_30" "EMA_40"
## [10] "Altcoin_EMA_40" "DASH" "DOGE"
## [13] "ETC" "ETH" "LTC"
## [16] "SC" "XEM" "XMR"
## [19] "XRP" "ZEC" "CLF"
## [22] "CNYUSDX" "DJI" "EURUSDX"
## [25] "GCF" "GSPC" "IXIC"
## [28] "JPYUSDX" "TSLA" "VIX"
## [31] "XWDTO" "Cost_per_TR" "Num_TR_per_Block"
## [34] "Bu_Be_Spread_MA8" "SMA_05" "SMA_90"
## [37] "EMA_05" "EMA_90" "MACD"
## [40] "Avg_Dir_Mvmt" "RSI" "Awesome_Osc"
## [43] "ROC" "Stoch_RSI" "Ultimate_Osc"
## [46] "True_SI" "Cum_Return" "Log_Return"
## [49] "Number_of_Transactions" "Active_Addresses" "New_Addresses"
## [52] "Hash_Rate" "sentiment_elon" "sentiment_bitcoin"
# Read United BTC Dataset (used in the Python Modelling)
btc <- read_csv('bitcoin_full_daily_returns.csv')
##
## -- Column specification --------------------------------------------------------
## cols(
## .default = col_double(),
## Date = col_date(format = ""),
## sentiment_elon = col_character(),
## sentiment_bitcoin = col_character()
## )
## i Use `spec()` for the full column specifications.
names(btc)
## [1] "Date" "WeightedPrice_return" "DASH_return"
## [4] "DOGE_return" "ETC_return" "ETH_return"
## [7] "LTC_return" "SC_return" "XEM_return"
## [10] "XMR_return" "XRP_return" "ZEC_return"
## [13] "CLF_return" "CNYUSDX_return" "DJI_return"
## [16] "EURUSDX_return" "GCF_return" "GSPC_return"
## [19] "IXIC_return" "JPYUSDX_return" "TSLA_return"
## [22] "VIX_return" "XWDTO_return" "Volume"
## [25] "SMA_30" "EMA_40" "Altcoin_EMA_40"
## [28] "Cost_per_TR" "Num_TR_per_Block" "Bu_Be_Spread_MA8"
## [31] "SMA_05" "SMA_90" "EMA_05"
## [34] "EMA_90" "MACD" "Avg_Dir_Mvmt"
## [37] "RSI" "Awesome_Osc" "ROC"
## [40] "Stoch_RSI" "Ultimate_Osc" "True_SI"
## [43] "Cum_Return" "Log_Return" "Number_of_Transactions"
## [46] "Active_Addresses" "New_Addresses" "Hash_Rate"
## [49] "sentiment_elon" "sentiment_bitcoin"
# Create Time series Dataset
# Create original time series Dataset
bit_ts = bitcoin %>%
filter(Date > as.Date('2017-01-01')) %>%
arrange(Date) %>%
select(WeightedPrice) %>%
as.matrix() %>%
ts()
# Create time series from BTC returns Dataset
bit_ret_ts = btc %>%
filter(Date > as.Date('2017-01-01')) %>%
arrange(Date) %>%
select(WeightedPrice_return) %>%
as.matrix() %>%
ts()
# Plot BTC Prices (full Dataset)
# Plot BTC Data
ggplotly(ggplot(bitcoin, aes(Date, WeightedPrice)) + geom_line(col = '#ffa500') +
labs(title = 'Bitcoin Weighted Prices 2014 -2021', x = '') +
scale_y_continuous(breaks = c(0, 5000, 10000, 15000, 30000, 60000),
labels = c('$0', '$5,000', '$10,000', '$15,000',
'$30,000', '$60,000')) + my_theme)
# Plot BTC Prices after 2017
ggplotly(bitcoin %>%
filter(Date > as.Date('2017-01-01')) %>% ggplot(aes(Date,
WeightedPrice)) +
geom_line(col = '#ffa500') +
labs(title = 'Bitcoin Weighted Prices after 2017', x = '') +
scale_y_continuous(breaks = c(0, 5000, 10000, 15000, 30000, 60000),
labels = c('$0', '$5,000', '$10,000', '$15,000',
'$30,000', '$60,000')) + my_theme)
# Correlation plots for BTC Prices & its lags
gglagplot(bit_ts, do.lines = F) + my_theme +
scale_color_continuous(low = "#b37400", high = "#ffc04d",
breaks = c(1, 366, 731, 1097, 1463),
labels = c('2017', '2018', '2019', '2020', '2021')) +
scale_y_continuous(breaks = c(0, 5000, 10000, 15000, 30000, 60000),
labels = c('$0', '$5,000', '$10,000', '$15,000',
'$30,000', '$60,000')) +
scale_x_continuous(breaks = c(5000, 10000, 15000, 30000, 60000),
labels = c('$5,000', '$10,000', '$15,000',
'$30,000', '$60,000'))
# Autocorrelation (ACF) and Partial Autocorrelation (PACF) plots
ggAcf(bit_ts, lag.max = 200) + my_theme + labs(title = 'ACF' , y = 'Correlation')
ggPacf(bit_ts, lag.max = 200) + my_theme + labs(title = 'PACF', y = '')
# Autocorrelation (ACF) and Partial Autocorrelation (PACF) after differencing
ggAcf(diff(bit_ts), lag.max = 200) + my_theme +
labs(title = 'ACF with First Differnce' , y = 'Correlation')
ggPacf(diff(bit_ts), lag.max = 200) + my_theme +
labs(title = 'PACF with First Difference', y = '')
# Autocorrelation (ACF) and Partial Autocorrelation (PACF) with daily returns
ggAcf(bit_ret_ts, lag.max = 200) + my_theme +
labs(title = 'ACF with Daily Returns' , y = 'Correlation')
ggPacf(bit_ret_ts, lag.max = 200) + my_theme +
labs(title = 'PACF with Daily Returns', y = '')
# Plot First Difference after 2017
cut_bit_df = bitcoin %>%
filter(Date > as.Date('2017-01-01'))
ggplotly(cut_bit_df[-1,] %>%
mutate(WeightedPrice = diff(cut_bit_df$WeightedPrice)) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#ffa500') +
my_theme + labs(x = '', title = 'Bitcoin Differenced By One',
y = 'Difference'))
# Plot Daily Returns after 2017
cut_bit_ret_df = btc %>%
filter(Date > as.Date('2017-01-01'))
ggplotly(cut_bit_ret_df[-1,] %>%
mutate(WeightedPrice_return = diff(
cut_bit_ret_df$WeightedPrice_return)) %>%
ggplot(aes(Date, WeightedPrice_return)) + geom_line(col = '#ffa500') +
my_theme + labs(x = '', title = 'Bitcoin Daily Returns',
y = '% Returns'))
# Box-Cox Normalization of Bitcoin Prices
BoxCox.lambda(bit_ts)
## [1] -0.03727455
ggplotly(cut_bit_df %>%
mutate(WeightedPrice = BoxCox(cut_bit_df$WeightedPrice,
lambda=BoxCox.lambda(
cut_bit_df$WeightedPrice))) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#ffa500') +
my_theme + labs(x = '', title = 'Bitcoin Box-Cox transformed',
y = 'BTC Price Transformed'))
# Plot First Difference, Transformed First Difference & Daily Returns
## Original Price
cut_bit_df[-1,] %>%
mutate(WeightedPrice = diff(cut_bit_df$WeightedPrice)) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#650fba') + my_theme +
labs(x = '', title = 'Original BTC Price', y = 'Difference')
## Transformed Price
cut_bit_df[-1,] %>%
mutate(WeightedPrice = diff(BoxCox(cut_bit_df$WeightedPrice,
lambda = BoxCox.lambda(
cut_bit_df$WeightedPrice)))) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#650fba') + my_theme +
labs(x = '', title = 'Transformed BTC Price', y = '')
## Daily Returns of Price
cut_bit_ret_df[-1,] %>%
ggplot(aes(Date, WeightedPrice_return)) + geom_line(col = '#650fba') + my_theme +
labs(x = '', title = 'Daily Returns of BTC Price', y = '')
# Autocorrelation (ACF) and Partial Autocorrelation (PACF) transformed Prices
bit_ts_tran = BoxCox(bit_ts, lambda = BoxCox.lambda(bit_ts))
ggAcf(diff(bit_ts_tran), lag.max = 200) + my_theme + labs(title = 'ACF' , y = 'Correlation')
ggPacf(diff(bit_ts_tran), lag.max = 200) + my_theme + labs(title = 'PACF', y = '')
# Test for Stationarity
# Daily Prices Dataset
adf.test(bit_ts) # p-value < 0.05 indicates the TS is stationary
##
## Augmented Dickey-Fuller Test
##
## data: bit_ts
## Dickey-Fuller = -1.6865, Lag order = 11, p-value = 0.711
## alternative hypothesis: stationary
# Box-Cox Transformed Dataset
adf.test(bit_ts_tran) # p-value < 0.05 indicates the TS is stationary
##
## Augmented Dickey-Fuller Test
##
## data: bit_ts_tran
## Dickey-Fuller = -2.1671, Lag order = 11, p-value = 0.5076
## alternative hypothesis: stationary
# Daily Returns Dataset
adf.test(bit_ret_ts) # p-value < 0.05 indicates the TS is stationary
## Warning in adf.test(bit_ret_ts): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: bit_ret_ts
## Dickey-Fuller = -10.475, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationary
# Try an Autoarima with transformed data
arima_tr <- auto.arima(bit_ts_tran)
checkresiduals(arima_tr)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(3,1,1) with drift
## Q* = 8.1023, df = 5, p-value = 0.1507
##
## Model df: 5. Total lags used: 10
# Try an Autoarima with daily returns data
arima_ret <- auto.arima(bit_ret_ts)
checkresiduals(arima_ret)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,0,2) with non-zero mean
## Q* = 10.711, df = 6, p-value = 0.09773
##
## Model df: 4. Total lags used: 10
# Taking only 2020
cut2_bit_df = cut_bit_df %>%
filter(Date >= ymd('2020-01-01'))
ggplotly(cut2_bit_df %>%
mutate(WeightedPrice = BoxCox(cut2_bit_df$WeightedPrice,
lambda = BoxCox.lambda(
cut2_bit_df$WeightedPrice))) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#ffa500') +
labs(title = 'Bitcoin', x = '', y = 'Price (Transformed)') + my_theme)
ggplotly(cut2_bit_df[-1,] %>%
mutate(WeightedPrice = diff(BoxCox(cut2_bit_df$WeightedPrice,
lambda = BoxCox.lambda(
cut2_bit_df$WeightedPrice)))) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#ffa500') +
my_theme + labs(x = '', title = 'Transformed Price', y = 'Difference'))
# ACF, PCF only for 2020
bit_ts2 = bitcoin %>%
filter(Date >= as.Date('2020-01-01')) %>%
arrange(Date) %>%
select(WeightedPrice) %>%
as.matrix() %>%
ts()
bit_ts_tran2 = BoxCox(bit_ts2, lambda = BoxCox.lambda(bit_ts2))
ggAcf(diff(bit_ts_tran2), lag.max = 200) + my_theme + labs(title = 'ACF' ,
y = 'Correlation')
ggPacf(diff(bit_ts_tran2), lag.max = 200) + my_theme + labs(title = 'PACF', y = '')
# Autoarima for Data only 2020
arima_2020_tr <- auto.arima(bit_ts_tran2)
checkresiduals(arima_2020_tr)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,1) with drift
## Q* = 14.894, df = 8, p-value = 0.06123
##
## Model df: 2. Total lags used: 10
# Taking only 2021
cut3_bit_df = cut_bit_df %>%
filter(Date >= ymd('2021-01-01'))
ggplotly(cut3_bit_df %>%
mutate(WeightedPrice = BoxCox(cut3_bit_df$WeightedPrice,
lambda = BoxCox.lambda(
cut3_bit_df$WeightedPrice))) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#ffa500') +
labs(title = 'Bitcoin', x = '', y = 'Price (Transformed)') + my_theme)
ggplotly(cut3_bit_df[-1,] %>%
mutate(WeightedPrice = diff(BoxCox(cut3_bit_df$WeightedPrice,
lambda = BoxCox.lambda(
cut3_bit_df$WeightedPrice)))) %>%
ggplot(aes(Date, WeightedPrice)) + geom_line(col = '#ffa500') +
my_theme + labs(x = '', title = 'Transformed Price', y = 'Difference'))
# ACF, PCF only for 2021
bit_ts3 = bitcoin %>%
filter(Date >= as.Date('2021-01-01')) %>%
arrange(Date) %>%
select(WeightedPrice) %>%
as.matrix() %>%
ts()
bit_ts_tran3 = BoxCox(bit_ts3, lambda = BoxCox.lambda(bit_ts2))
ggAcf(diff(bit_ts_tran3), lag.max = 200) + my_theme + labs(title = 'ACF' ,
y = 'Correlation')
ggPacf(diff(bit_ts_tran3), lag.max = 200) + my_theme + labs(title = 'PACF', y = '')
# Autoarima for Data only 2021
arima_2021_tr <- auto.arima(bit_ts_tran3)
checkresiduals(arima_2021_tr)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0)
## Q* = 13.409, df = 10, p-value = 0.2017
##
## Model df: 0. Total lags used: 10
# ARIMA Model Fits
## Data after 2017
bit_ts_past_2017 = bitcoin %>%
filter(Date >= as.Date('2017-01-01')) %>%
arrange(Date) %>%
select(WeightedPrice) %>%
as.matrix() %>%
ts()
bit_ts_past_2017 %>%
BoxCox(lambda = BoxCox.lambda(bit_ts_past_2017)) %>%
Arima(order = c(0,1,0), include.drift = T) %>%
checkresiduals()
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0) with drift
## Q* = 81.859, df = 9, p-value = 6.894e-14
##
## Model df: 1. Total lags used: 10
summary(Arima(bit_ts_tran, order = c(0,1,0), include.drift = T))
## Series: bit_ts_tran
## ARIMA(0,1,0) with drift
##
## Coefficients:
## drift
## 0.0016
## s.e. 0.0006
##
## sigma^2 estimated as 0.000653: log likelihood=3626.59
## AIC=-7249.18 AICc=-7249.17 BIC=-7238.41
##
## Training set error measures:
## ME RMSE MAE MPE MAPE
## Training set 3.788572e-06 0.02553818 0.01755831 -1.606423e-05 0.2328859
## MASE ACF1
## Training set 0.9947251 0.2064681
## Daily Return Data after 2017
bit_ts_ret_past_2017 = btc %>%
filter(Date >= as.Date('2017-01-01')) %>%
arrange(Date) %>%
select(WeightedPrice_return) %>%
as.matrix() %>%
ts()
bit_ts_ret_past_2017 %>%
Arima(order = c(0,1,0), include.drift = T) %>%
checkresiduals()
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0) with drift
## Q* = 262.58, df = 9, p-value < 2.2e-16
##
## Model df: 1. Total lags used: 10
summary(Arima(bit_ret_ts, order = c(0,1,0), include.drift = T))
## Series: bit_ret_ts
## ARIMA(0,1,0) with drift
##
## Coefficients:
## drift
## 0.0000
## s.e. 0.0011
##
## sigma^2 estimated as 0.002042: log likelihood=2707.03
## AIC=-5410.07 AICc=-5410.06 BIC=-5399.3
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 2.741485e-08 0.04516154 0.03086297 85.18454 445.309 0.9993754
## ACF1
## Training set -0.3749845
## Random Walk Test on Daily Data only 2020
bit_ts_tran2 %>%
Arima(order = c(0,1,0), include.drift = T) %>%
checkresiduals()
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0) with drift
## Q* = 32.082, df = 9, p-value = 0.0001927
##
## Model df: 1. Total lags used: 10
summary(Arima(bit_ret_ts, order = c(0,1,0), include.drift = T))
## Series: bit_ret_ts
## ARIMA(0,1,0) with drift
##
## Coefficients:
## drift
## 0.0000
## s.e. 0.0011
##
## sigma^2 estimated as 0.002042: log likelihood=2707.03
## AIC=-5410.07 AICc=-5410.06 BIC=-5399.3
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 2.741485e-08 0.04516154 0.03086297 85.18454 445.309 0.9993754
## ACF1
## Training set -0.3749845
## Random Walk Test on Daily Data only 2021
bit_ts_tran3 %>%
Arima(order = c(0,1,0), include.drift = T) %>%
checkresiduals()
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0) with drift
## Q* = 13.43, df = 9, p-value = 0.1441
##
## Model df: 1. Total lags used: 10
summary(Arima(bit_ret_ts, order = c(0,1,0), include.drift = T))
## Series: bit_ret_ts
## ARIMA(0,1,0) with drift
##
## Coefficients:
## drift
## 0.0000
## s.e. 0.0011
##
## sigma^2 estimated as 0.002042: log likelihood=2707.03
## AIC=-5410.07 AICc=-5410.06 BIC=-5399.3
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 2.741485e-08 0.04516154 0.03086297 85.18454 445.309 0.9993754
## ACF1
## Training set -0.3749845
# Check errors
# Transformed Data
err_tr = residuals(Arima(bit_ts_tran, order = c(0,1,0), include.drift = T))
cat('Standard Deviation = ', sd(err_tr))
## Standard Deviation = 0.02554609
cat('Mean =', mean(err_tr))
## Mean = 3.788572e-06
invers_BoxCox = function(ts_data, lambda){
original_ts = (ts_data * lambda + 1) ** (1/lambda)
return(original_ts)
}
invers_BoxCox(sd(err_tr), BoxCox.lambda(bit_ts))
## [1] 1.025888
# Daily Return Data
err_ret = residuals(Arima(bit_ret_ts, order = c(0,1,0), include.drift = T))
cat('Standard Deviation = ', sd(err_ret))
## Standard Deviation = 0.04517554
cat('Mean =', mean(err_ret))
## Mean = 2.741485e-08
invers_BoxCox(sd(err_ret), BoxCox.lambda(bit_ret_ts))
## Warning in guerrero(x, lower, upper): Guerrero's method for selecting a Box-Cox
## parameter (lambda) is given for strictly positive data.
## [1] 1.045235
# Forecast with ARIMA
## h is the the length you want the prediction to be in units of days
fit_model = function(bitcoin_data, h){
bitcoin_df = bitcoin_data %>%
filter(Date >= as.Date('2017-01-01')) %>%
arrange(Date)
time_series = bitcoin_df %>%
select(WeightedPrice) %>%
ts()
predictions = time_series %>%
BoxCox(lambda = BoxCox.lambda(time_series)) %>%
auto.arima() %>%
forecast(h)
forecast_df = cbind(data.frame(predictions[4]),
data.frame(predictions[5]),
data.frame(predictions[6]))
the_forecast = invers_BoxCox(forecast_df, lambda = BoxCox.lambda(time_series))
the_forecast = the_forecast %>%
mutate(Date = tail(bitcoin_df$Date, h) + h) %>%
as_tibble()
return(the_forecast)
}
# read the updated data for BTC prices
bitcoin_new <- read_csv('btc_base_dataset_NEW.csv')
##
## -- Column specification --------------------------------------------------------
## cols(
## .default = col_double(),
## Date = col_date(format = ""),
## Day_of_Week = col_character()
## )
## i Use `spec()` for the full column specifications.
# Plot the new BTC Data
ggplotly(ggplot(bitcoin_new, aes(Date, WeightedPrice)) +
geom_line(col = '#ffa500') +
labs(title = 'Bitcoin Weighted Prices 2014 -2021 (new)', x = '') +
scale_y_continuous(breaks = c(0, 5000, 10000, 15000, 30000, 60000),
labels = c('$0', '$5,000', '$10,000', '$15,000',
'$30,000', '$60,000')) + my_theme)
## Predict the BTC Price for the next 30 Days
ggplotly(fit_model(bitcoin, 30) %>%
ggplot(aes(x = Date, y = mean)) + geom_line(col = '#ff2500') +
geom_ribbon(aes(ymin = lower.80., ymax = upper.80.), alpha = .3,
fill = '#ffc04c') +
geom_ribbon(aes(ymin = lower.95., ymax = upper.95.), alpha = .3,
fill = '#ffe4b2') +
geom_line(data = bitcoin_new, aes(Date, WeightedPrice)) +
geom_line(data = filter(bitcoin, Date >= as.Date('2015-01-01')),
aes(Date, WeightedPrice), col = '#ffa500') + my_theme +
labs(title = 'Bitcoin Prediction of 30 Days', y = 'Price', x = '') +
scale_y_continuous(breaks = c(0, 5000, 10000, 15000, 20000, 25000,
30000, 35000, 40000, 45000, 50000,
55000, 60000),
labels = c('$0', '$5,000', '$10,000', '$15,000',
'$20,000', '$25,000', '$30,000',
'$35,000', '$40,000', '$45,000',
'$50,000', '$55,000', '$60,000')))